Other Seminars
Special activity of the Hitchin-Ngô Laboratory
Speaker: Nigel Hitchin (University of Oxford), Mario García-Fernández (ICMAT-CSIC) ()Date: Monday, 12 January 2026 - 10:00-12:30Place: Aula Naranja, ICMAT
Abstract:
10:00 - 11:00. Nigel Hitchin (University of Oxford)
Title: A universal Higgs bundle moduli space
Abstract: It has long been known that the hyperkähler metric on the moduli space of Higgs bundles over a curve C is completely determined by a single function on the character variety, effectively the norm square of the associated Higgs field. Using this function and its dependence on the complex structure of C, we give a differential-geometric construction of the universal Higgs bundle moduli space as a complex manifold fibred over Teichmüller space, endowed with a Hermitian metric. A key feature is a natural symplectic Ehresmann connection.
11:00 - 11:30.Coffee break
11:30 - 12:30. Mario Garcia-Fernandez (ICMAT-CSIC)
Title: Universal Hitchin moduli spaces
Abstract: We study metric aspects of the universal moduli space of solutions to Hitchin's equations as the complex structure varies over the Teichmüller space of a closed surface. Our approach is gauge theoretical, and builds on the theory of Kähler fibrations and the moment map interpretation of constant scalar curvature Kähler metrics. We will consider two families of moduli spaces, first from the theory of G-Higgs bundles and then taking the viewpoint of flat G-connections. We will comment on a conjectural relationship between them, inspired by the twistor geometry of Hitchin's hyperkähler moduli space. Joint work with L. Álvarez-Cónsul, O. García-Prada, and S. Trautwein, arXiv:2512.07553.
